A. G. B. Lauder and D. Wan. Computing zeta functions of Artin-Schreier curves over finite fields II. To appear in a special issue of the Journal of Complexity, 2002. Home/Search Document Details and Download
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An Extension of Kedlaya's Algorithm to Artin-Schreier.. - Denef, Vercauteren (2002) (1 citation) (Correct)
....proof of the rationality of the zeta function and leads to a polynomial time algorithm for computing the zeta function of an arbitrary variety over a nite eld. Despite its polynomial complexity, the algorithm in its most general form is not practical. Using Dwork cohomology, Lauder and Wan [16] adapted their original algorithm for the special case of Artin Schreier curves, resulting in an O(g q) time algorithm. In this paper we extend Kedlaya s algorithm to Artin Schreier curves de ned by an equation of the form y y f(x) 0 over some nite eld F q of characteristic 2. The ....
.... curve e C m;f over a nite eld F q with q = 2 elements, can be computed deterministically in ) bit operations with space complexity O(g ) 5 Implementation and Numerical Results In this section we compare the eciency of our algorithm with an algorithm by Lauder and Wan [16], which also runs in O(g ) bit operations and needs ) storage space. As far as we know, Lauder Wan s algorithm has not been implemented before. Table 1 presents running times of our algorithm and Lauder Wan s algorithm for genus 2 and genus 3 Artin Schreier curves over various nite ....
A.G.B. Lauder and D. Wan. Computing zeta functions of Artin-Schreier curves over nite elds. Preprint 2001.
An Extension of Kedlaya's Algorithm to Hyperelliptic Curves .. - Denef, Vercauteren (2002) (Correct)
....a nite eld. Note that Wan [37] suggested the use of p adic methods, including the method of Dwork and Monsky, already several years ago. Despite the polynomial time complexity of the Lauder and Wan algorithm, it is not practical for cryptographical sizes. Using Dwork cohomology, Lauder and Wan [19] adapted their original algorithm for the special case of Artin Schreier curves, resulting in an O(g ) time algorithm. In [6] we described an extension of Kedlaya s algorithm to Artin Schreier curves in characteristic 2 which has the same time complexity O(g ) In this paper we extend ....
A.G.B. Lauder and D. Wan. Computing zeta functions of Artin-Schreier curves over nite elds. London Mathematical Society JCM, 5:34-55, 2002.
Counting Points on Varieties over Finite Fields of Small.. - Lauder, Wan (2001) (3 citations) Self-citation (Lauder Wan) (Correct)
No context found.
A.G.B. Lauder and D. Wan, Computing zeta functions of Artin-Schreier curves over nite elds, London Math. Soc. JCM, Vol. 5, (2002), 34-55.
Computing Zeta Functions of Artin-Schreier Curves over Finite II - Lauder, Wan (2002) (10 citations) Self-citation (Lauder Wan) (Correct)
.... counting points on a special class of curves based upon part of this theory, namely MonskyWashnitzer cohomology for smooth ane varieties [11] The authors have also developed fast methods for other classes of curves using the so called Dwork cohomology, and more generally Dwork Reich cohomology [13, 15]. Date: September 27, 2002. Alan Lauder gratefully acknowledges the support of the EPSRC (Grant GR N35366 01) and St John s College, Oxford. Daqing Wan is partially supported by the NSF. Mathematics Subject Classi cation 2000: 11Y16, 11T99, 14Q15 Key words and phrases: Artin Schreier curve, ....
....sheaf on the curve, whereas we use one for the L function of non constant sheaves (Artin Schreier and Kummer) on open subsets of the projective line. Thus in our approach the complication lies in the sheaf, while with Kedlaya it lies in the base variety. In this paper we extend the work of [15] to arbitrary ArtinSchreier covers of the projective line. We only give details for a restricted class of curves, but these are sucient to cover a large class of hyperelliptic curves in characteristic 2, which is the main motivation behind the work. Such curves are of interest in cryptography ....
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A.G.B. Lauder and D. Wan, Computing zeta functions of Artin-Schreier curves over nite elds, London Mathematical Society, JCM, Vol. 5, 2002, 34-55.
Counting Points on C_ab Curves Using Monsky-Washnitzer.. - Denef, Vercauteren (2004) (Correct)
No context found.
A. G. B. Lauder and D. Wan. Computing zeta functions of Artin-Schreier curves over finite fields II. To appear in a special issue of the Journal of Complexity, 2002.
Counting Points on C_ab Curves Using Monsky-Washnitzer.. - Denef, Vercauteren (2004) (Correct)
No context found.
A. G. B. Lauder and D. Wan. Computing zeta functions of Artin-Schreier curves over finite fields. LMS J. Comput. Math., 5:34--55 (electronic), 2002.
Computing Zeta Functions Of Curves Over Finite Fields - Vercauteren (2003) (1 citation) (Correct)
No context found.
A. G. B. Lauder and D. Wan. Computing zeta functions of Artin-Schreier curves over nite elds II. To appear in a special issue of the Journal of Complexity, 2002.
Computing Zeta Functions Of Curves Over Finite Fields - Vercauteren (2003) (1 citation) (Correct)
No context found.
A. G. B. Lauder and D. Wan. Computing zeta functions of Artin-Schreier curves over nite elds. LMS J. Comput. Math., 5:34-55 (electronic), 2002.
An Extension of Kedlaya's Algorithm to Hyperelliptic Curves .. - Denef, Vercauteren (2004) (Correct)
No context found.
A.G.B. Lauder and D. Wan. Computing zeta functions of Artin-Schreier curves over finite fields II. Journal of Complexity, 20:331--349, 2004.
An Extension of Kedlaya's Algorithm to Hyperelliptic Curves .. - Denef, Vercauteren (2004) (Correct)
No context found.
A. G. B. Lauder and D. Wan. Computing zeta functions of Artin-Schreier curves over finite fields. LMS J. Comput. Math., 5:34--55 (electronic), 2002.
Computing Zeta Functions of Hyperelliptic Curves over Finite.. - Vercauteren (2002) (4 citations) (Correct)
No context found.
A.G.B. Lauder and D. Wan. Computing zeta functions of Artin-Schreier curves over finite fields. London Mathematical Society JCM, 5:34--55, 2002.
An Extension of Kedlaya's Algorithm to Hyperelliptic Curves .. - Denef, Vercauteren (2002) (Correct)
No context found.
A.G.B. Lauder and D. Wan. Computing zeta functions of Artin-Schreier curves over nite elds. London Mathematical Society JCM, 5:34-55, 2002.
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